Implication

If two propositions pp and qq can be combined into statements of form: If p, then q, the statement is considered an implication.

Denoted by pqp \rightarrow q

Latex: pqp \rightarrow q

Let pp: it will rain tomorrow. qq: i will get wet if I go outside

If it will rain tomorrow, I will get wet if I go outside.

Since the statement contains a condition, it is called a conditional statement.

The component pp is the hypothesis (or premise) of the implication, and q is the conclusion.

Implications occur in a number of ways:

If p, then q If p, q p implies q p only if q q if p p is sufficient for q q is necessary for p

Note: only pp only if qq does not have the same mean ing as "p if q". "p if q" has the same meaning as "If q, then p"

Converse, contrapositive and inverse

Let pp and qq be propositions and AA the conditional statement pqp \rightarrow q

Converse

The proposition qpq \rightarrow p is the converse of A

Contrapositive

The proposition ¬q¬p\neg q \rightarrow \neg p is the Contrapositive of A.

Inverse

The proposition ¬p¬q\neg p \rightarrow \neg q is the inverse of A